g-CN體系的準粒子能帶結(jié)構(gòu)和光學特性

梁冬梅　冷　霞　馬玉臣,*

(1山東大學化學與化工學院，濟南250100；2凱里學院物理與電子工程學院，貴州凱里556011)

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g-CN體系的準粒子能帶結(jié)構(gòu)和光學特性

梁冬梅1,2冷霞1馬玉臣1,*

(1山東大學化學與化工學院，濟南250100；2凱里學院物理與電子工程學院，貴州凱里556011)

利用多體格林函數(shù)理論，本文研究了二維CN體系(包括triazine和tri-s-triazine)的激發(fā)態(tài)特性。通過GW方法，我們計算了準粒子的能量?？紤]電子－空穴相互作用，通過求解Bethe-Salpeter方程，我們獲得了激發(fā)態(tài)能量和光譜。我們發(fā)現(xiàn)，在這兩種CN體系的價帶中，σ軌道和π軌道之間的交換作用非常強烈。由于占據(jù)的σ軌道和π軌道之間的準粒子修正量非常不同，因此，為了得到準確的帶隙值和光譜，我們需要對這兩種軌道開展精確的GW計算。與單層的CN體系相比，雙層結(jié)構(gòu)中層與層之間的范德華相互作用使帶隙值降低了0.6 eV，而光吸收譜紅移了0.2 eV，這是由于雙層結(jié)構(gòu)具有更小的激子束縛能。我們計算的吸收峰的位置與實驗結(jié)果符合很好。實驗中的吸收峰主要是由深能級的π軌道到π*軌道的躍遷形成的。π→π*躍遷和σ→π*躍遷之間的耦合能夠在長波長范圍產(chǎn)生弱的吸收尾巴，如果調(diào)整入射光的極化方向，由σ→π*躍遷產(chǎn)生的高強度的吸收峰將會在更低能量處出現(xiàn)。

g-CN；準粒子能帶結(jié)構(gòu)；光譜；躍遷；多體格林函數(shù)理論

www.whxb.pku.edu.cn

1　Introduction

Carbon nitride(C3N4)has recently attracted wide attention due to its potential applications in optoelectronics and mechanical devices1,2.There are five kinds of allotropes of C3N4,including α-C3N4,β-C3N4,cubic-C3N4,pseudocubic-C3N4,and graphitic-C3N4. Among them,graphitic carbon nitride(g-C3N4)is considered to possess the highest stability under ambient conditions3,4.Generally, g-C3N4has two types of structural isomers,triazine(Fig.1(a))and tri-s-triazine(Fig.1(b))which are constructed by their primary heterocyclic building blocks.Generally,monolayer g-C3N4constructing from triazine is labeled as g-CN1,while the one constructing from tri-s-triazine is refered to as g-CN2,respectively. Theoretical studies have shown that g-CN2 is more stable than g-CN1 by about 30 kJ·mol－1 5.

g-CN2 can act as a metal-free polymetric photocatalyst,and has exhibited high activity in splitting water to produce hydrogen under visible-light irradiation6.However,pure g-CN2 can only absorb light with the wavelength shorter than 450 nm,which may limit its solar energy utilization efficiency.Although g-CN1 can also be applied in splitting water,it can only absorb UV light(less than 250 nm)7.

To improve photocatalytic activity of these materials,great efforts have been taken to expand visible-light absorption range. Doping,as one of the effective strategies,has been employed to modify the electronic structures of semiconductor,including nonmetallic and metallic doping.For example,the productivity rate of H2has been improved more than 7.2－8.0 times through sulfur doping compared to pure g-C3N43.Zn doping in g-C3N4can also enhance the photocatalytic activity and increase H2productivity rate8.However,the recombination rate of photo-generated carriers increases at the defect centers,which is unfavorable for photocatalytic process.Although much experimental work has been done to study the photocatalytic properties of g-CN,little is known about the excited states dynamics process in the water splitting. Photon-induced water splitting process,such as in the natural photosynthetic centers,is very complicated,since many kinds of excited states are involved in the energy transfer and charge transfer between water and the photocatalysts.Although the solar energy is absorbed at the optical spectrum peaks,the states that are really responsible for the photocatalytic process may be some dark excited states that are dipole-forbidden under light irradiation9.So in order to find out the dynamics mechanism of water splitting on g-CN,it is necessary to study in detail the excited states of g-CN first.

Fig.1　Primitive cells of g-CN

Some theoretical calculations on the electronic structure and optical absorption spectrum of g-CN have been performed by firstprinciples methods including GW method,Bethe-Salpeter equation(BSE),and density functional theory(DFT)with various exchange correlation functions,such as local density approximation,generalized gradient approximation,and the hybrid functional HSE0310.Xu11and Wei12et al.used GW method to calculate the quasiparticle(QP)structures of g-CN1 and g-CN2, however,their band gaps differ by a large amount(~1.3 eV)from each other.Wei et al.12also calculated the optical spectra of g-CN2 by Bethe-Salpeter equation,however,there is about 0.7 eV deviation between their calculated optical peak and the experimental one13.This error is far beyond the typical accuracy of BSE method and there must be something missed in their calculations.So it is quite necessary to investigate the band structures and optical properties of g-CN once again by high-level first principles approaches in order to get a correct understanding of this material.

In this paper,we employed the state-of-the-art many-body Green's function theory,including GW method and Bethe-Salpeter equation(GW+BSE)14－17,to study quasiparticle band structures and optical absorption of monolayer g-CN1,g-CN2 and bilayer g-CN1,g-CN2.GW+BSE have successfully been applied to investigate electronic and optical properties of many low dimensional materials,such as monolayer MoS218,graphene19,carbon nanotube20,etc.In this work,we got very good optical spectra for these graphitic carbon nitrides that are in agreement with experiments,which warrants reasonable descriptions of excited states in these materials.We will present in the following the marked difference in the exchange-correlation potentials and the difference in the contribution to the optical absorption between σ orbitals and π orbitals.We will also discuss the strong effects of interlayer interaction on the exciton binding energy and optical absorption.

2　Models and methods

Geometries of g-CN1 and g-CN2 are optimized with DFT using the Vienna ab initio Simulation Package(VASP)code21,22,employing the generalized gradient approximation(GGA)of Perdew-Wang 91 functional23.A 3.5 nm vacuum gap is added in the perpendicular direction of the g-CN surface in order to remove theinteraction between adjacent images.A6×6×1 Monkhorst-Pack k-point mesh is employed for DFT calculations.

AGaussian-orbital based code15－17is used to perform the GW+ BSE calculations.This code has been applied in materials like carbon nanotubes20,24,and organic molecules like DNA25.Kohn-Sham eigenvalues and eigen-wave functions,which are calculated within local density approximation(LDA)in this work,are used to construct operators in GW and BSE.Dielectric function is calculated by random-phase approximation and the plasmon-pole model15.17×17×1 and 10×10×1 k-point meshes are used for g-CN1 and g-CN2 to represent the exciton wavefunctions in BSE, which can converge the excitation energy within 0.05 eV.In the calculations of dielectric function and self-energy operator,a scissor shift is added to the Kohn-Sham eigenvalues.The magnitude of the scissor shift is adjusted until it equals the difference between the quasiparticle band gap and the DFT-LDAone.

The BSE Hamiltonian takes the form of H=(ECQP－EVQP)+Keh, where ECQP－EVQPis the energy difference between conduction bands(C)and valence bands(V)which are calculated by GW method,Kehis the electron－h(huán)ole interaction kernel.EQPis the quasiparticle energy calculated by GW method including valence bands and conduction bands.Since there is a large difference in quasiparticle corrections between σ and π orbitals,we calculated EQPexplicitly for all the 289 k points of g-CN1 and 100 k points of g-CN2 in BSE.This is necessary to get accurate spectra.If this effect is not taken into account,the error in the absorption peak can amount to 1.1 eV.

3　Results and discussion

The lattice constants of g-CN1 and g-CN2 are 0.477 and 0.712 nm,respectively,which are in agreement with the experimental values of 0.47026and 0.713 nm6.

Table 1 lists the calculated band gaps of g-CN1 and g-CN2 by DFT and GW methods,and Fig.2 shows their band structures. Although the DFT values from different research groups are close to each other,the agreement in the GW band gaps from different groups is bad.g-CN2 is more stable than g-CN1,and it is the most widely studied g-CN material.The real electronic band gap of g-CN2 has never been announced in any literature,instead the optical band gap measured in the experiments has been falselyassigned as the electronic band gap6,13.However,the optical spectrum of g-CN2 has been well established and could be a good model to test the quality of theoretical calculations.

Table 1　Band gaps(in eV)of g-CN by different approaches

Fig.2　Band structures of monolayer g-CN

3.1g-CN1

3.1.1monolayer g-CN1

For g-CN1,after quasiparticle correction by GW method,the dispersion of the bottom of the conduction bands changes little as shown in Fig.2.The lowest two conduction bands(a4 and a5 in Fig.2(a))are π*orbitals.Since there are lone pairs of electrons from nitrogen atoms in g-CN,the valence bands are composed by both σ and π orbitals.For example,the first and the third valence bands(a1 and a3 in Fig.2(a))are σ orbitals,while the second valence band(a2 in Fig.2(a))is of π character.There is a large difference in quasiparticle corrections to the σ and π orbitals.For example,in DFT-LDA,points k1,k2,and k3 in Fig.2(a)are well separated,but in GW points k1 and k2 become hybridized and degenerate in energy,while the gap between k2 and k3 is greatly enlarged as shown in Fig.2(b).The quasiparticle correction to the π orbital is 0.8 eV smaller than that to the σ orbital.By comparing the diagonal matrix elements of self-energy operator(Σ),including its exchange part(x)and correlation part(c),we found that at K point||for a2 is smaller than||for a3 by 3.54 eV,and||for a2 is smaller than||for a3 by 1.71 eV.Correct prediction of the energy of state a2 is important since the transition from it constitutes the optical peak observed in the experiments.At Г point, states a3 and a2 are degenerate,and both of them are of σ character.This degeneracy isn't broken in GW.Our GW gap is different from that gotten by Wei et al.in Ref.12 by 0.82 eV,while the GW gap by Xu et al.in Ref.11 is lower than ours by 2.09 eV.

Fig.3(a)is the optical absorption spectra of g-CN1 with the electric field of the light parallel to the g-CN1 surface(this will be denoted as E||s,where E and s represent the electric field and surface,respectively).If we do not consider the electron－h(huán)ole interaction,i.e.calculating the independent particle transition spectrum within GW approximation,the spectrum has a strong peak at 7.07 eV which is formed by the transition from π(mainly a2 in Fig.2(a))to π*(a4 and a5 in Fig.2(a))orbitals.The energy of this peak is close to that from Wei et al.in Ref.12.With electron－h(huán)ole interaction considered,the optical spectrum redshifts with the first prominent peak locating at 4.65 eV(denoted as s1a). Above 6.0 eV,there is a significant peak at 6.98 eV(denoted as s1b).States s1a and s1b are formed by the transitions from π→π*and σ→π*with the former dominating.

Fig.3　Optical absorption spectra of monolayer g-CN calculated by GW+BSE method with(red solid lines)and without(blue dashed lines)electron－h(huán)ole interaction

Till now,there is no experimental optical absorption spectrumof g-CN1 in vacuum.The only experimental spectrum of g-CN1 is that measured in water solution by Khabashesku et al.in Ref.7. In water solution,g-CN1 has a strong absorption peak at 4.96 eV. This energy differs from our calculated s1a state by 0.31 eV, moreover,the overall shape of the calculated spectrum deviates from the experimental one since there is another strong peak at s1b state in our calculations.Water molecule may distort the structure of g-CN through strong electrostatic interaction between hydrogen atom in H2O and nitrogen atom in g-CN as studied by Aspera et al.in Ref.27 through first principles calculations.These effects influence the optical spectrum,and could explain the difference between our calculated spectrum and the experimental one.

At the low-energy side of the s1a peak there are also many states which have very weak oscillator strengthening when E||s. These states originate from the combination of σ→π*and π→π*transitions with the former predominating.Since the σ orbital is symmetric with respect to the g-CN1 plane,while the π*orbital is antisymmetric with respect to the g-CN1 plane,the direction of the transition dipole moment<σ|r→|π*>is along the normal of the g-CN1 plane.So when electric field of the light is perpendicular to the g-CN1 surface(E⊥s),the σ→π*transitions can acquire strong oscillator strengths.Fig.3(b)is the calculated optical spectrum for the case of E⊥s.There emerges a weak absorption peak at 3.15 eV(denoted as s1c),which is consistent with the experimentally observed weak absorption peak at 410 nm7.

From the point of view of exciton binding energy(Eb),the excited states in g-CN1 can be classified into two types,i.e.tightlybound electron-hole pair and loosely-bound one.For example,the states s1a and s1c belong to the former type with the binding energies of 2.57 and 2.63 eV,respectively.Fig.4(a)and(b)show the real-space distributions of electron and hole for the s1a exciton,while Fig.4(c)and(d)are those for the s1c exciton.We can see that both excitons are localized,with their radius about 0.6 nm. Apparently,transition from the π(σ)orbitals on nitrogen atoms to the π*orbitals constitutes the s1a(s1c)exciton.For comparison, Fig.4(e)and(f)show the real space distributions of a looselybound exciton at 4.64 eV whose binding energy is 0.74 eV.This exciton is highly-delocalized.It is formed predominantly by σ→π*transitions.The energy of this exciton is lower than that of s1a. After optical absorption at s1a,the system may decay nonradiatively to this loosely-bound excitonic state where carriers(electron and hole)separate more easily.

3.2g-CN2

3.2.1monolayer g-CN2

Fig.4　Real-space distribution of electron(red solid surfaces in left panels)and hole(purple solid surfaces in right panels)for the excited states in monolayer g-CN1

g-CN2 is an indirect-gap semiconductor with the conduction band minimum(CBM)at K point and the valence band maximum (VBM)at Г point(Fig.2(c)and(d)).The direct and indirect band gaps are 5.67 and 4.56 eV by our GW calculations,respectively. Our DFT-LDAband gaps are close to those by Wei et al.12,while our quasiparticle gaps are larger than theirs by 0.4 eV.In DFT,we classified the valence bands within 3.5 eV to the VBM into four groups as denoted by u1,u2,u3,and u4 in Fig.2(c).Orbital analysis of them indicates that u1,u4 and two orbitals in u2 are σ states formed by lone-pair electrons of nitrogen atoms,while u3 and one orbital in u2 originate from the π states.Quasiparticle corrections to σ states are 0.8 eV on average larger than those to π states in g-CN2.We took the band energies at Г point as an example.In DFT,points Г2 and Г5 are both twofold degenerate with σ character,Г3 and Г4 are π states.The order between Г2 and Г3 exchanges from DFT-LDAto GW.The gap between Г1,which is a σ state,and Г3 decreases from 0.95 eV to 0 eV.The gap between Г4 and Г5 is enlarged by 1.09 eV,at the same time a band below u4 upshifts becoming hybridized with it at Г5 point.Experimentally,through optical absorption spectrum the band gap of g-CN2 has been assigned to 2.7 eV6,13.This energy is in fact the onset of the optical absorption.In the following,it will be shown that this energy could be given a reasonable explanation through theoretical spectra from BSE.

Fig.3(c)is the optical spectrum of g-CN2 with E||s.Without electron－h(huán)ole interaction,the independent-particle GW spectrum exhibits a prominent peak at 5.88 eV which originates from π→π*transition.This is 0.6 eV smaller than the result from Wei et al.12,which can be attributed to the underestimation of GW band gaps and quasiparticle corrections to the π orbitals.If the electronhole interaction is considered,the spectrum has a strong peak at3.84 eV(denoted as s2a in Fig.3(c))and a weak peak at 2.66 eV (denoted as s2b in Fig.3(c)).This energy of s2b state is close to the onset(2.7 eV)of optical absorption of g-CN2 as measured in experiments6,13.The lowest excited state is at 2.58 eV(denoted as s2c in Fig.3(c))and is dipole-forbidden.The energy of the s2a peak is in agreement with Wei et al.in Ref.12,while it is larger than that of the experimental absorption peak6,13.This may be attributed to the influence of light polarization direction.To demonstrate this effect on the optical absorption of g-CN2,in next section we will discuss the optical spectrum of g-CN2 with E⊥s. States s2a and s2b both come from the σ→ π*and π→ π* transitions.In s2a,π→π*has the same weight as σ→π*,while in s2b,σ→π*predominates.Fig.5(a)and(b)show the real-space distribution of exciton in the s2a state.Excitons of both s2a and s2b are localized,with the exciton binding energy more than 1.5 eV.

Excitons composed by σ→π*transitions can be activated when the light polarization direction is perpendicular to the g-CN2 surface as shown in Fig.3(d)for the corresponding optical spectrum.For example,a new peak(denoted as s2d)emerges at 3.45 eV,and the state s2c also becomes weakly allowed.The energy of the s2d peak is in agreement with the experimental results(~375 nm)6,13.Excitons in states s2c and s2d are both localized in real space as shown in Fig.5(c)and(d)for the latter.The exciton binding energy for s2d is 2.52 eV.In contrast to g-CN1,at the lowenergy side of s2a there is no state with very small exciton binding energy(<1 eV).This kind of state only emerges above 4.15 eV. In the next section,we will see that loosely-bound excitons are available for bilayer g-CN2 at the low-energy side of the absorption peak.

Fig.5　Real-space distribution of electron(red solid surfaces in left panels)and hole(purple solid surfaces in right panels)for the excited states in monolayer g-CN2

In addition,for monolayer g-CN1 and g-CN2,our calculations differ from those of Wei et al.in Ref.12 in two aspects.On the one hand,we took partial self-consistent GWcalculations,i.e.a scissor shift,whose value is tuned until it equals the difference between the GW band gap and DFT-LDAband gap,is added to the singleparticle eigenvalues in the evaluation of dielectric function and Green′s function，while Wei et al.obtained the quasiparticle energies non-self-consistently,i.e.by one-shot G0W0calculations.On the other hand,in our BSE calculations,all the 289 k points of g-CN1 and 100 k points of g-CN2 were explicitly calculated since there is a large difference in quasiparticle corrections between σ and π orbitals,while Wei et al.did not take these ingredients into account.

3.2.2bilayer g-CN2

g-CN2 used in experiments usually contains many layers.It is necessary to investigate the influence of interlayer interaction on its electronic and optical properties.Here,we studied bilayer g-CN2 as the example.The distance between the two layers is fixed to the theoretical value of 0.329 nm28,29.We chose the configuration where C atoms of the top layer are on the top of N atoms of bottom layer as shown in Fig.1(d).This kind of configuration is more stable than the one where C(N)in one layer and C(N)atoms in another layer locate against each other30.Fig.6(c)and(d)show the band structures of bilayer g-CN2 obtained from DFT-LDAand GW.From monolayer to bilayer,the overall shape of the band structure changes little.Just like monolayer g-CN2,an indirect band-gap can be found with the VBM at the Г point and the CBM at the K point.The direct(Г→Г)and indirect gap(Г→K)for bilayer g-CN2 calculated by DFT-LDA are 2.01 and 1.06 eV, respectively,and those by GW are 5.10 and 4.05 eV,respectively. The difference in DFT-LDAgaps between monolayer and bilayer g-CN2 is small(~0.1 eV),but the difference in quasiparticle gaps are large(0.57 eV for direct and 0.51 eV for indirect gaps).In bilayer g-CN2,the lowest six conduction bands are composed by π*orbitals,and the valence bands are composed by σ and π orbitals just like monolayer g-CN2.Quasiparticle corrections to σ orbitals are 0.81 eV larger than those to π orbitals.

Fig.7(c)gives optical absorption spectrum of bilayer g-CN2 with E||s.Without taking electron－h(huán)ole interaction into account, the spectrum has a significant peak at 5.51 eV that originates fromπ→π*transition.This peak redshifts by 0.37 eV with respect to that of the monolayer g-CN2.This is consistent with the fact that the band gap of bilayer g-CN2 is smaller than that of monolayer g-CN2.By taking electron－h(huán)ole interaction into account,a prominent absorption peak emerges at 3.69 eV(denoted as s3a) as shown in Fig.7(c).By inspecting real-space distribution of excitons for this peak(not shown here),we found that the peak has the same character as the peak s2a in monolayer g-CN2,with the difference that exciton s3a reside in different layer.This energy redshifts by 0.15 eV with respect to the absorption peak of monolayer g-CN2,which is smaller than that variation of the band gap.This reduced redshift is induced by the alleviated excitonbinding energy in bilayer g-CN2 compared to that in monolayer g-CN2 as a result of the increased electronic screening in bilayer g-CN2.

Fig.6　Band structures of bilayer g-CN

There are also some very weakly-allowed excited states at the low-energy side of s3a which come from the combination of π→π*and σ→π*transitions just like monolayer g-CN2,such as the peak at 2.58 eV which is not shown in Fig.7(c).However,in contrast to monolayer g-CN2,there exist some excitons with weak binding energies(~1 eV)at the lower energy side of the absorption peak for bilayer g-CN2.For example,Fig.8 show the realspace distributions of this kind of delocalized excitons at 3.53 and 3.58 eV.The hole in the former occupies σ orbitals in one layer, while in the latter a majority of the hole occupies σ orbitals in one layer and some occupies π orbitals in another layer.

For the case of E⊥s,when the electron－h(huán)ole interaction is considered,the absorption has a strong peak at 3.11 eV(denoted as s3b in Fig.7(d))which originates from the dipole-allowed σ→π*transition.We should notice that pure π→π*transitions cannot create excitons with energies lower than 2.5 eV in perfect bilayer g-CN2.Excitation below 2.5 eV can only occur when σ→π* transitions take part in.The polarization direction of light used in experiments is random.Optical absorption in experiments must contain contribution from both σ→π*and π→π*transitions. The combination of these two kinds of transitions,with the former predominating,can account for the absorption tail below 2.7 eV as found in the experiments6,13.

Comparing monolayer and bilayer g-CN2,optical absorption maximum in the latter extends more into the visible range by 0.34 eV than the former when E⊥s,i.e.the latter can absorb more visible light than the former.Moreover,one shortcoming of monolayer g-CN2 is that its exciton binding energy is very high, while the electron-hole pairs in bilayer g-CN2 is relatively easy to dissociate since there are some excited levels with small exciton binding energy in the low-energy side of the absorption maximum. Excitons created at the absorption maximum may decay nonradiatively to these loosely-bound excitonic levels.An ideal photocatalyst should have both a wide visible absorption range and weak excitonic binding energy.Some progress has been made in fabricating efficient graphitic carbon nitride photocatalysts for water splitting,such as embedding graphite nanoparticles into g-CN2 as reported by Liu et al.in Ref.13,although the mechanism for improvement of photocatalytic capability is still unclear.

3.2.3Bilayer g-CN1

For comparison,we also investigated the influences of interlayer interaction on the electronic and optical properties of bilayer g-CN1 at the structure shown in Fig.1(c).The distance between the two layers is set to the optimized value of 0.336 nm which is close to the experimental data31,32.Fig.6(a)and(b)show the band structures of bilayer g-CN1 obtained by DFT-LDAand GW.From monolayer to bilayer,the overall shape of the band structures from DFT-LDA to GW changes little.Just like monolayer g-CN1,a direct band gap in bilayer g-CN1 can be found with the VBM andCBM both at Г point.The gaps for bilayer g-CN1 calculated by DFT-LDA and GW are 1.40 and 4.44 eV,respectively.The difference between monolayer and bilayer g-CN1 in DFT-LDA is only 0.16 eV,while the difference in quasiparticle gaps are up to 0.62 eV.Just like monolayer g-CN1,in bilayer g-CN1 the lowest four conduction bands are composed by π*orbitals and the valence bands are composed by σ and π orbitals.Quasiparticle corrections to σ orbitals are 0.56 eVlarger than those to π orbitals.

Fig.7　Optical absorption spectra of bilayer g-CN calculated by GW+BSE method with(red solid lines)and without(blue dashed lines)electron－h(huán)ole interaction

Fig.8　Real-space distribution of electron(red solid surfaces in left panels)and hole(purple solid surfaces in right panels)for some delocalized excited states in bilayer g-CN2

Fig.9　Real-space distribution of electron(red solid surfaces in left panels)and hole(purple solid surfaces in right panels)for some delocalized excited states in bilayer g-CN1

Fig.7(a)shows the optical spectra of bilayer g-CN1 with E||s. Without electron-hole interaction,a prominent absorption peak located at 6.60 eV is found that originates from π→π*transition, which redshifts by 0.47 eV with respect to monolayer g-CN1.This variation is in agreement with the change that the quasiparticle gap of bilayer g-CN1 is smaller than that of monolayer g-CN1.By taking electron－h(huán)ole interaction into account,a strong peak emerges at 4.37 eV(denoted as s4a),which is shown in Fig.7(a). This energy redshifts by 0.28 eV compared to the absorption peak of monolayer g-CN1,which is smaller than that change of the band-gap.Compared to the redshift of the optical absorption peak in monolayer g-CN1,the reduced shift in bilayer g-CN1 is induced by the alleviated exciton binding energy owing to the increased electronic screening in it.

Just like monolayer g-CN1,at the lower energy side of the absorption peak for bilayer g-CN1,there are some excitons with weak binding energies(<1 eV).For example,the real-space distributions of this kind of delocalized excitons at 4.00 eV and 4.23 eV are shown in Fig.9.For the case of E⊥s,when electronhole interaction is taken into account,a strong absorption peak at 2.83 eV(denoted as s4b)can be seen in Fig.7(b),which originates from the dipole-allowed σ→π*transition.

4　Conclusions

In summary,we studied the electronic structures and optical properties of two graphitic carbon nitrides by the first-principles GW+BSE method.The calculated BSE spectra for g-CN1 and g-CN2 agree well with the experiments.We provide more reliable results than previous GW and BSE calculations.We found that the electronic band gap of g-CN2(or C3N4used in other literature)is not 2.7 eV,but 5.67 eV(4.56 eV)for the direct(indirect)band gap instead.The electronic band gap and optical absorption maximum of graphitic carbon nitrides are controlled by different valence orbitals,σ for the former and π for the latter.However,the absorption tail in the long-wavelength range is determined by transitions related to σ orbitals which might be also responsible for the dissociation of carriers(electron and hole).

Increasing the thickness of graphitic carbon nitrides,e.g.using bilayer one,not only can redshift the optical absorption maximum, but the exciton binding energy is decreased due to the increase of electronic screening,which is favorable for carrier dissociation. Thereby,designing photocatalysts should take both optical absorption range and electronic screening into account.We think that this rule might be also applicable to other two-dimensional materials,such as MoS2,BN,WS233.

The dependence of spectrum and also water-splitting behavior on the light polarization direction has never been studied by experiment for g-CN.With E||s,the absorption maximum of monolayer(bilayer)g-CN2 is lower in energy than that of g-CN1 by 0.81(0.68)eV.If E⊥s,the difference in the position of the first prominent peak between g-CN2 and g-CN1 reduces to 0.3 eV.

Acknowledgment:We thank the National Supercomputing Center in Jinan for providing Computational resources.

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Quasiparticle Band Structures and Optical Properties of Graphitic Carbon Nitrides

LIANG Dong-Mei1,2LENG Xia1MAYu-Chen1,*
(1School of Chemistry and Chemical Engineering,Shandong University,Jinan 250100,P.R.China;
2College of Physics and Electronic Engineering,Kaili University,KaiLi 556011,Guizhou Province,P.R.China)

The excited-state properties of two-dimensional carbon nitrides,including triazine and tri-s-triazine, were investigated using many-body Green′s function theory.Their quasiparticle energies were calculated with the GW method.By solving the Bethe-Salpeter equation(BSE),which takes into account electron－h(huán)ole interactions,excitation energies and optical spectra were obtained.Strong interactions,mainly originating from exchange interactions,were found between σ and π orbitals in the valence bands of the two carbon nitrides. The quasiparticle corrections for occupied σ and π orbitals are quite different,so both of them need to be calculated at the level of the GW method to obtain accurate results for both band gaps and optical spectra from the BSE.Compared with monolayer carbon nitrides,interlayer van der Waals interactions in bilayer systems lower the band gap by 0.6 eV,while the optical absorption spectrum red shifts by 0.2 eV.This is because of the smaller exciton binding energy in bilayer systems.Our calculated positions of the absorption peaks are in good agreement with experiments.The absorption peaks in experiments are dominated by transitions from deep π orbitals to π*orbitals.Coupling between π→π*and σ→π*transitions can lead to a weak absorption tail in the long wavelength region.If we tune the polarization direction of the incident light,new strong absorption peaks originating from σ→π*transitions emerge at lower energies.

Graphitic carbon nitride;Quasiparticle band structure;Optical spectrum;Transition; Many-body Green′s function theory

March 2,2016;Revised:April 28,2016;Published on Web:April 29,2016.

O649

10.3866/PKU.WHXB201604292

*Corresponding author.Email:myc@sdu.edu.cn;Tel:+86-531-88363138.

The project was supported by the National Natural Science Foundation of China(21173130,21433006,21573131).

國家自然科學基金(21173130,21433006,21573131)資助項目

?Editorial office ofActa Physico-Chimica Sinica

［Article］